Problem: Simplify the following expression: $ y = \dfrac{9t}{t + 7} - \dfrac{-3}{8} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{9t}{t + 7} \times \dfrac{8}{8} = \dfrac{72t}{8t + 56} $ Multiply the second expression by $\dfrac{t + 7}{t + 7}$ $ \dfrac{-3}{8} \times \dfrac{t + 7}{t + 7} = \dfrac{-3t - 21}{8t + 56} $ Therefore $ y = \dfrac{72t}{8t + 56} - \dfrac{-3t - 21}{8t + 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{72t - (-3t - 21) }{8t + 56} $ Distribute the negative sign: $y = \dfrac{72t + 3t + 21}{8t + 56}$ $y = \dfrac{75t + 21}{8t + 56}$